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We present a study of the structural phase transition, mechanical andthermodynamic properties of UO$_{2}$ by means of the local densityapproximation (LDA)$+U$ approach. A phase transition pressure of 40 GPa, whichagrees well with the experimental value of 42 GPa, is obtained from theory at 0K. Pressure-induced enhancements of elastic constants, elastic moduli, elasticwave velosities, and Debye temperature of the fluorite phase are observed.Phonon spectrums of both the ground state fluorite structure and high pressurecotunnite structure calculated by the supercell approach show that thecotunnite structure is dynamically unstable under ambient pressure. Based onthe imaginary mode along the $\Gamma$$-$$X$ direction and soft phonon modealong the $\Gamma$$-$$Z$ direction, a transition path from cotunnite tofluorite has been identified. We calculate the lattice vibrational energy inthe quasiharmonic approximation using both first-principles phonon density ofstate and the Debye model. Calculated temperature dependence of latticeparameter, entropy, and specific heat agree well with experimental observationsin the low temperature domain. The difference of Gibbs free energy between thetwo phases of UO$_{2}$ has predicted a boundary in the pressure-temperaturephase diagram. The solid-liquid boundary is approximated by an empiricalequation using our calculated elastic constants.

Phonon spectrum, thermodynamic properties, and pressure-temperature phase diagram of uranium dioxide